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Article pubs.acs.org/Langmuir
Mechanical History Dependence in Carbon Black Suspensions for Flow Batteries: A Rheo-Impedance Study Aditya Narayanan, Frieder Mugele, and Michael H. G. Duits* Physics of Complex Fluids Group, MESA+ Institute, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands S Supporting Information *
ABSTRACT: We studied the effects of shear and its history on suspensions of carbon black (CB) in lithium ion battery electrolyte via simultaneous rheometry and electrical impedance spectroscopy. Ketjen black (KB) suspensions showed shear thinning and rheopexy and exhibited a yield stress. Shear step experiments revealed a two time scale response. The immediate effect of decreasing the shear rate is an increase in both viscosity and electronic conductivity. In a much slower secondary response, both quantities change in the opposite direction, leading to a reversal of the initial change in the conductivity. Stepwise increases in the shear rate lead to similar responses in the opposite direction. This remarkable behavior is consistent with a picture in which agglomerating KB particles can stick directly on contact, forming open structures, and then slowly interpenetrate and densify. The fact that spherical CB particles show the opposite slow response suggests that the fractal structure of the KB primary units plays an important role. A theoretical scheme was used to analyze the shear and timedependent viscosity and conductivity. Describing the agglomerates as effective hard spheres with a fractal architecture and using an effective medium approximation for the conductivity, we found the changes in the derived suspension structure to be in agreement with our qualitative mechanistic picture. This behavior of KB in flow has consequences for the properties of the gel network that is formed immediately after the cessation of shear: both the yield stress and the electronic conductivity increase with the previously applied shear rate. Our findings thus have clear implications for the operation and filling strategies of semisolid flow batteries. as Ketjen black (KB) or Timcal SuperP.3,11 These carbon blacks are submicrometer-sized permanently fused aggregates of hollow spherical subunits.12,13 The self-assembly of the CNPs, which depends on their morphology, colloidal interactions, and shear conditions, is of crucial importance to both the electrical and mechanical performance of SSFBs. For colloidal carbon black (CB) units in SSFB media,3,5,11,14 the van der Waals attractions should be dominant because their electrostatic interactions are strongly screened.11,15 As a result, CB particles tend to form large cohesive structures. At rest (assuming a high enough concentration), they form a spacefilling network that can conduct electrons and suspend EAPs against gravity through yield stress.3,11 In flow (e.g., pumping and stirring), this network will be broken down into agglomerates. This leads to shear thinning and much lower electronic conductivity.3,11 Henceforth in this article we differentiate a permanently fused primary aggregate from a reversibly flocculated cluster of these particles, which we will call an agglomerate. Given the novelty of SSFBs, significant developments are still required to optimize their performance. Mechanical protocols
1. INTRODUCTION In light of climate change, recent years have seen a rapid adoption of renewable energy production.1 Because of their inherently variable nature, renewables have placed considerable strain on the power grid which must match energy production to demand. A possible solution to this problem is to store energy in batteries.2 Semisolid flow batteries (SSFBs), a recently developed configuration,3−10 are considered to be especially promising for such applications. SSFBs use two fluid electrodes, an anolyte and a catholyte, in place of traditional solid electrodes. The use of fluid electrodes decouples the energy of a SSFB, which depends on the size of storage tanks, from its power, which depends on the size of the reactor. Additionally, SSFBs may allow easy lifecycle management through the modification or replacement of their fluid electrodes. SSFB electrodes are mixtures of conductive nanoparticles (CNPs) and electrochemically active particles (EAPs) dispersed in an electrolyte solution. In most SSFBs, the EAPs intercalate and deintercalate lithium whereas the CNPs wire the EAPs to the current collectors. The continuous phase, a mixture of linear and cyclic carbonate solvents with a high concentration of dissolved lithium salt, provides an ionconducting medium and a source of lithium ions. The CNPs used in SSFBs are typically superconductive carbon blacks such © 2017 American Chemical Society
Received: December 1, 2016 Revised: January 18, 2017 Published: January 25, 2017 1629
DOI: 10.1021/acs.langmuir.6b04322 Langmuir 2017, 33, 1629−1638
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Langmuir should be a part of this optimization: fluids containing adhesive particles generally produce nonequilibrium structures that can depend on mechanical history.16−19 In this article, we focus on how shear and its history influence the electrical and rheological properties of CB suspensions in an SSFB solvent. Although the case of CB in an SSFB solvent is rather new,3,11,15 we anticipate that some existing insights into the behavior of CB suspensions will also be applicable to our system. Suspensions of reversibly agglomerating colloids, including those of CB, are known to be strongly shear- and history-sensitive.11,20−25 The storage modulus and yield stress of CB gels in oils have even been found to depend predictably on the preshear used to prepare them.23,24 In flow, the viscosity of agglomerating colloidal suspensions typically decreases in time after an increase in shear stress or rate, a well-studied property known as thixotropy.21,22 The opposite effect, a temporal increase in viscosity after an increase in shear stress or rate, known as rheopexy or antithixotropy, is much less common but has been observed in CB suspensions.23,26−28 On a mechanistic level, rheopexy is thought to be caused by flow-induced flocculation26 or by the ability of fractal structures to rearrange (when shear is lowered) into more densified agglomerates.23,24 The electrical impedance of CB suspensions in shear flow has been studied much less often, but also here a dependence on the shear rate was found.11,14,29 The study of the suspension’s rheology and impedance in conjunction capitalizes on the tight connection of both behaviors to the (dynamic) microstructure of the agglomerates, which can be difficult to measure with optical or scattering techniques, especially for concentrated suspensions. The present study makes use of a home-built rheoimpedance setup to characterize the influence of the mechanical history on both rheological and electrical properties. This approach addresses both the practical aspect of optimizing SSFB performance via mechanical protocols and the more fundamental aspect of understanding the underlying processes. Both stepwise changes in shear rate and prolonged shear are explored to identify transient responses. The cessation of shear is included as a special case, where the system is left with only Brownian forces to possibly reorganize its structure. Our analysis of the structural changes at the microscale is supported by a theoretical model in which the viscosity of effective hardsphere agglomerates30 is combined with an effective medium theory for the conductivity.31
Because the KB aggregates are highly porous and their subunits are hollow shells, the occupied volume fraction in suspension is much higher than wf. A crude estimate can be obtained by multiplying wf by the ratio of the density of graphite (2267 kg/m3) to the tap density of KB (100 kg/m3), giving a volume fraction of 23%. Particles were first wetted by the pure (binary) solvent in polypropylene containers. After 8 h, LiPF6 salt was added via a concentrated solution to bring its concentration to 1 M (viscosity 4 mPa·s32). After hand shaking, at least 8 h was allowed to let the particles equilibrate. Samples were then homogenized by rotor stator mixing (Ultraturrax) at 15 000 rpm for 2 min and subsequently loaded into the rheometer. In exploratory experiments, we found similar trends as reported in this article. However, the quantitative behavior of KB suspensions in SSFB media appeared to be sensitive to preparation protocols. This could be related to the poor wetting by the solvents, the sensitivity of the media,15 and the strong dependence of macroscopic properties on the volume fraction (S.I. Figure S1 and ref 11). Thus, for KB we performed all reported measurements (except those in Figure 4) on the same sample. 2.2. Rheoimpedance Measurements. Parallel rheological and electrical measurements on CB suspensions were performed on a stress-controlled Haake Rheostress RS600 rheometer with a homebuilt adaptation for electrical impedance spectroscopy (EIS) measurements (Figure 1). A 60-mm-diameter parallel plate geometry was
Figure 1. Schematic of rheo-impedance setup. (Gray) Measuring geometry with stationary lower and rotating upper plates. (Light gray) Mercury solvent trap. (Red) Sample. (Blue) Isolating dielectric. (Brown) Polypropylene body. (White) Cover. designed with both stainless steel plates also acting as electrodes. The rheometer rotates and measures torques on the upper geometry. To allow a frictionless low-noise electrical connection to the rotating plate, a mercury-based solvent trap was designed. A glass disk was used to electrically isolate the lower plate from the rheometer body. Because of its high thermal conductivity, glass also allows accurate temperature control (at 25 °C for all experiments). Argon was used to drive the rheometer air bearing. EIS was performed using a four-terminal configuration. The top plate was excited by a sinusoidal voltage, and the bottom was connected to the virtual ground of a transimpedance preamplifier (HF2TA, Zurich Instruments). A buffer preamplifier (HF2CA, Zurich Instruments) was used to measure the potential difference between the plates. An impedance spectroscope (HF2IS, Zurich Instruments) was used to extract the complex impedance from the current and voltage signals. AC frequency sweeps were performed from 10 to 100 MHz (total time 550 s) with a maximum applied voltage amplitude of ∼100 mV, which was within the linear response range of the samples. The frequency-dependent impedance of the empty measurement setup was calibrated out using the open short technique. Custom LabVIEW programs were used to synchronize rheological and electrical measurements. Rheo-impedance experiments were performed with a plate−plate gap of 250 μm. Suspensions of CB have been reported to exhibit nonideal rheometric behaviors such as wall slip, shear banding,23 and vorticity alignment of flocs,33 especially during start up and in lowshear-rate regimes. We avoided these effects in shear flow experiments
2. MATERIALS AND METHODS 2.1. Suspension Preparation. Ethylene carbonate (EC) and dimethyl carbonate (DMC) were obtained from Sigma-Aldrich (anhydrous, 99%+ purity). Binary mixtures of EC and DMC were 1:1 by mass. LiPF6 was purchased from Alfa Aesar (98% purity). Ketjen black EC 600JD powder (KB) was obtained from AkzoNobel (The Netherlands). Thermax N990 powder was donated by Cancarb. SEM samples were dispersed in acetone, dried on silica wafers, and then imaged. All other sample preparations and experiments were carried out in an MBraun argon-filled glovebox (O2, H2O below 5 ppm). The two types of CB used in this study differ in morphology (see also Figure 8): for N990, the unit particles are more or less compact spheres, whereas for KB, they are more fractal-like as a result of fusion between spherical subunits. In this article, we designate the KB units as aggregates, whereas clusters formed via reversible flocculation are called agglomerates. All suspensions of KB (of key interest for this work) were prepared at a concentration of 1% by weight (wf = 0.01). 1630
DOI: 10.1021/acs.langmuir.6b04322 Langmuir 2017, 33, 1629−1638
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Langmuir by employing relatively high shear rates, where the samples behave as low-viscosity liquids. To obtain a reproducible starting state (Figure 2),
of our KB suspension at rest can be analyzed with this approach. The very high frequencies (Figure 3 insets) are affected by uncompensated parasitics.36 Under strong shear, it is unlikely to have a continuous percolated network. (For low shear rates, dynamic percolation may be possible.37) However, a measurement at two frequencies on the same KB suspension, but now under high shear (open symbols of Figure 3), shows that the low-frequency real impedance is finite whereas the imaginary impedance is close to zero. This implies that the sheared suspension has a finite electronic resistance.35 Our measurements on other carbon black samples show that the overall impedance response under shear is similar in shape to that at rest (Figure S2 in S.I.), justifying our use of a single low frequency to probe the electronic resistance. Additionally, this is in qualitative agreement with earlier findings on carbon black filled polymers, which are known to conduct electrons via two mechanisms. (At high volume fractions, when the network is continuous, conduction is graphitic.38 The resistance is still determined by constriction and ohmic contributions.39) When the network is broken, the electrons can tunnel across small gaps (10 kHz). Filled symbols: KB at rest. Open symbols: KB under 1000 s−1 shear (only two frequencies measured). The 50 Hz points have been removed. 1631
DOI: 10.1021/acs.langmuir.6b04322 Langmuir 2017, 33, 1629−1638
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Figure 4. Intrinsic flow curve of agglomerates formed at different indicated shear rates (lines to guide the eye). The data point indicated by (x) represents the viscosity at 10 000 s−1 after prolonged shearing.
Figure 5. Evolution of viscosity and low-frequency real impedance of the KB suspension after a shear rate step from 316 to 100 (black), 177 (red), 562 (green), and 1000 s−1 (blue). The inset is a close-up view of the response of the electronic resistance around the step.
for PSR ≥ 1000 s−1: this again suggests that the agglomerates are largely broken down (i.e., into primary aggregates) by prolonged shear above 1000 s−1. Second, it becomes clear that in order to reach a steady state even the highest preshears need to be maintained for a significant duration, i.e., much longer than the data acquisition time (of O(1 s)) of the intrinsic flow curve. This is shown by the curves with PSR ≤ 316 s−1, for which the viscosities are different from the curves at higher PSRs, even for measurement shear rates ≥1000 s−1. Third, the fact that the intrinsic flow curves with smaller PSRs have lower viscosities is remarkable. In earlier suggested mechanistic pictures,30 where shear leads to both breakdown and the densification of agglomerates into smaller units, a lower PSRs should have resulted in higher viscosities, which is the opposite of what we observe. This points to a mechanism that can enhance the viscosity via agglomerate breakup in KB suspensions. The remarkable fact that the lowest possible viscosity (21 mPa·s) for our system was measured after the smallest preshear rate (100 s−1) also points in this direction. 3.2. Transient Behavior. To examine this intriguing behavior, we performed experiments in which the material’s response to shear rate steps was followed over time.21 Both the viscosity and the electronic resistance (Section 2.3) were measured in parallel. All steps in the shear rate were taken from the same reference condition, for which we chose 316 s−1, based on Figure 4. Some typical results of these measurements are found in Figure 5, where both steps up (to 562 and 1000 s−1) and down (to 177 and 100 s−1) are illustrated. Both the viscosity and the electronic resistance show a twostaged response. The initial response, a large increase in viscosity and a small decrease in electronic resistance for a step down in rate (transition from region I to region II) is fast, with a time scale of O(1 s). It is not resolvable, considering the short time that the rheometer needs to step the shear rate and the low frequency of the impedance measurement. For the steps to higher shear rates, the opposite trends were observed. The secondary response (region II) is significantly slower O (100−1000 s). The slow changes in the viscosity and resistance appear to have similar time scales, suggesting that they both probe changes in the microstructure of the KB. Remarkably, for both signals, the secondary response opposes the direction of the initial response. For the viscosity, this amounts to a relatively small correction (rheopexy, shear thinning), but for the electronic resistance, the secondary effect
is strong and causes a reversal of the overall effect. The shape of the decays of the viscosity and electronic resistance is well described by stretched exponentials; such behavior has been found for the viscosity of thixotropic systems.21 The opposing change in the second stage is found irrespective of whether the shear rate is increased or decreased. Yet the direction in which the shear rate is changed still determines the sign of all changes. This is consistent with a picture in which all structural transitions can be reversed via the shear rate. 3.3. Mechanistic Picture. We interpret our findings in Figures 4 and 5 with a picture in which KB reversibly agglomerates via two distinct mechanisms (each with its own time scale and influence on the microstructure). Both the viscosity and electronic resistance depend on the concentration and morphology of the agglomerates, but in different ways. Flow curves of weakly agglomerating suspensions have been successfully described by modeling the agglomerates along with their immobilized solvent as effective hard spheres.40,44 Shear thinning is then explained via a lowering of the effective hard sphere volume fraction. As the shear rate is increased, higher shear stress causes the agglomerates to break down into smaller structures. Because of the fractal build up, the latter then occupy less total volume (Figure 6). Although (strictly speaking) perfectly fractal scaling is rarely observed, it is has often been found that the structure of agglomerates can be fairly well described with this concept.30,40,43,44 To understand the (changes in) electronic conductivity of the suspension under flow, we need to take into account the formation of (transient) pathways with missing links (Figure 6, left). As such gaps dominate the resistance (Section 2.3), the macroscopic electronic resistance of the sheared suspension should be determined by the concentration of agglomerates and their typical distance of closest approach. We now proceed to a qualitative interpretation of Figure 5, focusing first on the instant process. The jumps in viscosity and electronic resistance may be explained by agglomeration due to lower shear forces when the rate is stepped down. The immediate sticking between colliding fractal entities leads to more open agglomerates that enclose (and hence immobilize) more solvent, causing the hydrodynamic volume fraction and thus the suspension viscosity to increase. (Note: if the shear step were small, then a binary collision would lead to an unstable agglomerate, which would be quickly eroded.) The same 1632
DOI: 10.1021/acs.langmuir.6b04322 Langmuir 2017, 33, 1629−1638
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Figure 6. Cartoon of fractal agglomeration and imperfect percolation (left) in shear flow.
interpenetration should lead to an overall densification of agglomerates, leading to a lower hydrodynamic volume fraction and hence a reduced viscosity. It also follows from mass conservation that the average gap between agglomerates will increase in this scenario. Additionally, the number of conduction pathways will decrease. Both effects should lead to the observed increase in the electronic resistance (after a stepdown in shear rate). The dependence of the interpenetrating agglomeration on shear rate can be understood as follows: the stability of interpenetrating KB units will depend on how deeply they are lodged within the agglomerate because only the peripheral zone will be exposed to local shear flow. This explains why a complete reversal of the process can only be achieved at high shear rates: here, the shear stresses are high and the agglomerates are small, thus exposing all KB units to shear. (This is also why we defined our samples by preshearing them at 10000 s−1.) In our proposed mechanism of interpenetrating agglomeration, the shape of the KB units plays an important role. To test this hypothesis, we performed an experiment comparable to that in Figure 5 but now with spherical unit particles (N990). This system was also strongly shear-thinning, indicating reversible agglomeration. A weight fraction of 30% was chosen to achieve a high shear viscosity similar to that of KB. Assuming that the hydrodynamic volume fractions of both suspensions are comparable when they are broken down to the unit particles, the only relevant difference should be the shape of the unit particle (Figure 8). The electrical resistance of the N990 suspensions turned out to be too high to be accessible at experimental frequencies (
